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2010 International Conference on Computational Intelligence and Communication Systems 2010 International Conference on Computational Intelligence and Communication Networks Prime Number Based Interleaver for Multiuser Iterative IDMA Systems Ruchir Gupta, B.K. Kanaujia R.C.S. Chauhan, M. Shukla, Member IEEE Department of Electronics & Communication Engineering Department of Electronics Engineering Ambedkar Institute of Technology Harcourt Butler Technological Institute Delhi, India Kanpur, India ruchir.in@gmail.com manojs@hbti.ac.in Abstract—In recently proposed multiple access techniques such each user. The system performance seriously degrades when as IDMA and OFDM-IDMA, the user separation is done by user the interleaving patterns are not orthogonal to each other i.e. specific interleavers in contrast to conventional CDMA scheme the collision among the interleaving patterns is not minimum. where user separation is assured with user-specific signature These interleavers disperse the coded sequences so that the sequences. The user specific interleavers must demonstrate adjacent chips are approximately uncorrelated, which facilitates minimum probability of collision amongst each other in addition the simple chip-by-chip detection. In case of interleavers in to other merits including minimal consumption of bandwidth, IDMA systems, the parameters such as ease of generation, least hardware for their generation, and least memory hardware required, bandwidth consumption during requirement. Previously, random interleaver and other transmission, and memory requirement at transmitter and interleavers proposed by researchers is still leaving some space receiver end, may be vital parameters for generation of for further research leading to optimality of interleavers. In this paper, we propose a novel interleaver based on prime numbers orthogonal interleavers. The greater the size of interleaver the for generation of user specific interleavers to remove the problem more it consumes the memory and extra bandwidth for of high consumption of bandwidth. The simulation results transmission, this becomes a greater problem when the number demonstrate the optimal performance of prime interleaver (PI) of users increase. In [2], random interleaver has been utilized in apart from other merits in comparison to random and other IDMA systems, while in [4], an efficient technique for interleavers. interleaver generation in IDMA has been proposed in. The second section highlights the IDMA systems model. In Keywords- prime numbers; computational complexity; third section, concepts of interleaving scheme along with interleaving; bandwidth requirement; memory requirement; various orthogonal interleavers are presented. In section 4, the orthogonality. proposed prime interleaver has been demonstrated while in section 5, the simulation results are demonstrated. I. INTRODUCTION II. IDMA MECHENISM By researchers, significant amount of research has been done in the field of wireless communication. The recently IDMA does not involve signature sequences, which greatly developed techniques including iterative multi user detection simplifies the problem of computational complexity in the (MUD) techniques for suppressing multiple access interference receiver. The major difference between IDMA and CDMA is (MAI) [1-2] has also drawn their attention. Interleave division regarding chip-level interleaving and bit level interleaving multiple access (IDMA) and OFDM-IDMA are the two respectively. It can be analyzed that the performance advantage multiple access (MA) schemes that make use of the iterative of IDMA increases with the number of users when compared to MUD efficiently, [3]. In IDMA, interleavers are being CDMA [1-2]. employed as the only means of user separation while in CDMA In multipath channels, adjacent chips from each user the signature sequences were designed to be means of user interferes each other. In CDMA, the bits are spreaded and then separation as the spreader provides no coding gain [3]. With passed with the same interleaver and transmitted consecutively, even random interleavers, the IDMA system performs similarly so the corresponding log-likelihood ratios (LLRs) are heavily and even better than a comparable CDMA system [2]. IDMA correlated. In IDMA, however chip level interleaving is outperforms CDMA in terms of better immunity to multiple performed. After random chip level interleaving, the replicas access interference (MAI) and higher user count. IDMA also are dispersed more randomly, so the corresponding LLRs inherits the advantages of CDMA such as asynchronous become less correlated. transmission, diversity against fading and cross cell interference mitigation at a reduced cost of complexity [3] and In order to minimize the forward error correction (FEC) high data rate. This chip by chip turbo type detection technique code rate IDMA transmitter is employed. The key principle of in IDMA also reduces the complexity of receiver multi use IDMA is that the interleavers {Пk} should be user-specific i.e. detector (MUD) as compared to that used in CDMA system [2- the cross correlation between specific interleavers must me 3]. minimum [7]. It is assumed that the interleavers are generated independently and randomly. These interleavers disperse the The efficiency of IDMA system is dependent on the coded sequences so that the adjacent chips are approximately generation of various pseudo random interleaving patterns for 978-0-7695-4254-6/10 $26.00 © 2010 IEEE 603 DOI 10.1109/CICN.2010.119 uncorrelated, which facilitates the simple chip-by-chip detection scheme. ζ k ( j ) = r ( j ) − hk x k ( j ) = ∑h k' xk ' ( j ) + n ( j ) k' ≠k is the distortion in r( j) with respect to user-k. The output of ESE and DECOD-DESPREEADERs block is given as [2] r ( j ) − E ( r ( j )) + hk E ( xk ( j )) eESE ( xk ( j )) = 2 hk . 2 Var ( rj ) − hk Var ( xk ( j )) S eDEC ( xk (π ( j ))) = ∑ eESE ( xk (π ( j ))) j =1 where j = 1,..., S Figure 1. Iterative IDMA Transmitter and Receiver III. VARIOUS ORTHOGONAL INTERLEAVERS FOR IDMA Fig. 1 presents the transmitter and receiver structure of the SCHEME multiple access scheme under consideration with K The principle of traditional periodic interleaving scheme simultaneous users. The input data sequence dk of user-k is which is suitable to block codes can be expressed by encoded based on a low-rate code C, generating a coded interleaving the data of array I × n. Let the interleaving degree sequence ck [ck(1), . . . , ck(j), . . . , ck(J)], where J the frame may be I for n bits. At the initial step, (I,n) linear block codes length. The elements in ck are referred to as coded bits. The are arranged in rows in an array I × n. Now, we transmit the coded bits are further spreaded over entire bandwidth with the array column by column. At the receiver, the received data are help of spreader. The spreader may be counted to be common rearranged in the same array column by column, then decoding or user specific. In this case, we have considered the spreader it rank by rank. to common to all the users. Then ck is permutated by an interleaver k, producing xk [xk(1), . . . , xk(j), . . . , xk(J)]. In theory, the user-specific interleavers are generated Following the CDMA convention, we call the elements in xk independently and randomly [2], known as random interleavers “chips”. Users are solely distinguished by their interleavers; (RI). In this case, the base station (BS) has to employ a hence the name interleave-division multiple-access considerable amount of memory to store these interleavers at (IDMA).The chip interleavers allow adopting a chip – by-chip transmitter and receiver side, which may cause serious concern estimation technique [2]. in case of large user count. Also, during the initial link setting- up phase, there should be messages passing between the BS At the receiver side, the outputs of the elementary signal and mobile stations (MSs) to inform each other about user estimator`s (ESE) and DECOD-DESPREEADERs are extrinsic specific interleavers. Extra bandwidth resource will be log-likelihood ratios (LLRs) about {xk }defined as [2] consumed for this purpose if the interleavers used by the BS and MSs are long and randomly generated. In [5], master random interleaver or power interleaver generation method is ⎛ p ( y / xk ( j ) = +1) ⎞ presented to alleviate this concern. With this method, the e( xk ( j )) = log ⎜ ⎟ , ∀k , j. (1) interleaver assignment scheme is simplified and memory cost ⎝ p ( y / xk ( j ) = −1) ⎠ is greatly reduced without sacrificing performance, but the complexity for regeneration of interleavers and deinterleavers These LLRs are further distinguished by the subscripts i.e., at the receiver side is major concern in case of higher user eSEB ( xk ( j )) and eDEC ( xk ( j )) , depending upon whether count [7] provided that enough memory space is not used to they are generated by ESE and DECOD-DESPREEADERs. store all required interleavers. Due to the use random interleavers {Π k}, the ESE Researchers has proposed various other interleavers in [8- operation can be carried out in a chip-by-chip manner, with 13][15][16]. PEG interleaver generation mechanisms [8] only one sample r(j) used at a time. The received signal at the explain the selection of suitable orthogonal interleavers out of receiver is given as pre-generated random interleavers while other mechanisms including [9-13], [15-16] explain the independent generation of orthogonal interleavers which are losing their orthogonality in r ( j ) = hk xk ( j ) + ζ k ( j ) (2) case of higher user count. In [7], tree base interleaver (TBI) generation scheme is presented which employs two master interleavers, which are randomly selected. User specific where interleaver is designed using a combination of both master 604 interleavers. The scheme is optimum in terms of bandwidth The bandwidth required by the Prime Interleaver (PI) is requirement and BER [14]; however, still there is space for smaller than other available interleavers as now only seed is to development of other efficient interleavers for IDMA scheme. be transmitted, in addition to very small amount of memory required at the transmitter and receiver side as shown in table Here, in this paper, a new interleaver is proposed based on 1. prime number which gives a novel user-specific interleaver generation mechanism with lesser time to get it generated and TABLE I COMPARISON OF BANDWIDTH REQUIREMENT FOR along with minimal consumption of bandwidth required during TRANSMISSION OF THE INTERLEAVING MASK transmission well similar performance in terms of BER to that User Random Tree Based Prime of random interleaver. Count Interleaver Interleaver Interleaver Generation Generation 2 2 2 1 IV. MECHANISM OF PRIME INTERLEAVER 6 6 2 1 In IDMA, different users are assigned different interleavers 14 14 2 1 which are weakly correlated. The computational complexity 30 30 2 1 and memory requirement should be small for generation of 62 62 2 1 interleavers. The Prime Interleaver is basically aimed to 126 126 2 1 minimize the bandwidth and memory requirement that occur in other available interleavers with bit error rate (BER) performance comparable to random interleaver. x 10 6 Comparison Graph showing Bandwidth Requirement of 4 Interleavers 5 In generation of prime interleaver we have used the prime Bandwidh requirement of Random Interleaver numbers as seed of interleaver. Here, user-specific seeds are 4.5 Bandwidth requirement of Master Random Interleaver Bandwidth requirement of Tree Based Interleaver B an dw idt h R eq uirem ent of Int erleav er(N o.of bits requ ired/u s e r) assigned to different users. 4 Bandwidth requirement of Prime Interleaver For understanding the mechanism of prime interleaver, let 3.5 us consider a case of interleaving n bits with seed p. First, we consider a Gallois Field GF (n). Now, the bits are interleaved 3 with a distance of seed over GF (n). In case, if {1, 2, 3, 5, 6, 7, 8… n} are consecutive bits to be interleaved with seed p then 2.5 location of bits after interleaving will be as follows 2 1===> 1 1.5 2===> (1+p) mod n 1 3===> (1+2p) mod n 0.5 4===> (1+3p) mod n 0 0 10 20 30 40 50 60 70 80 90 100 . . User Number . . Figure 2. Comparison of Bandwidth requirement of various interleavers . . In master random interleaving scheme the computational n===> (1+(n-1)p) mod n complexity and transmitter and receiver end is quite high due to calculation of user-specific intereleaving masks. The prime For Example if we have to interleave 8 bits such that {1, 2, interleaving scheme reduces the computational complexity that 3, 4, 5, 6, 7, 8} and we wish to interleave these bits with seed 3 occurs in master random interleaving scheme; however, it is then the new location of bit will be as follows higher to that of tree based interleaving scheme due 1===> 1 computation involved for calculation of user specific interleavers. 2===> (1+1*3) mod 3===>4 3===> (1+2*3) mod 3===>7 V. NUMERICAL RESULTS 4===> (1+3*3) mod 3===>2 For simplicity, IDMA system with BPSK signaling in 5===> (1+4*3) mod 3===>5 AWGN channel for hk=1, ∀ k is assumed. Without loss of generality, a uniform repetition coding CREP {+1, -1, +1, -1, ---- 6===> (1+5*3) mod 3===>8 -----} is used with spread length sl =16, for all users. In figure 3, uncoded IDMA cases are considered, i.e., without any 7===> (1+6*3) mod 3===>3 forward error correction (CFEC) coding while data length is 8===> (1+7*3) mod 3===>6 taken to be 512. In figure 5, Memory-2 Rate-1/2 Convolutional code is used. The iteration at the receiver side is chosen to be Now, the new order of bits will be {1, 4, 7, 2, 5, 8, 3, and 15 in each case. 6}. 605 From these figures, it is evident that the BER performances CDMA under same conditions, results are better with IDMA of IDMA scheme are similar for random and prime scheme as number of users is increased [2]. interleavers. But from figure 2, it is clear that, on the front of In figure 4, the coded IDMA for 16 users have been bandwidth consumption, the prime interleaver is outperforming presented along with results in uncoded as well coded IDMA the other interleavers because only the user specific prime environment. The result shows similar BER performances of numbers have to be sent along with data format during prime interleavers to random interleavers in coded as well transmission. uncoded IDMA environments. The simulation results for coded IDMA systems outperform the uncoded IDMA systems when 0 10 compared in terms of bit error rate (BER) performance. The prime interleaver is, however, performing similar to that of -1 random interlevers. 10 VI. CONCLUSION The proposed ‘Prime Interleaver’ is very easy to generate -2 10 Prime Interleaver 1 user Random Interleaver 1 user and is better than the random or any other interleavers in terms B it E rror Rate -3 Random Interleaver 4 users Prime Interleaver 4 users of bandwidth consumption problems. The Prime interleaver is better than master random interleaver in terms of 10 Random Interleaver 8 users Prime Interleaver 8 users Random Interleaver 16 users computational complexity. With tree based interleaver, the -4 10 Prime Interleaver 16 users proposed interleaver seems to be having little bit more Prime Interleaver 24 users Random Interleaver 24 users complexity due to involvement of higher calculation for Random Interleaver 32 users calculation of user-specific interleavers. -5 Prime Interleaver 32 users 10 Random Interleaver48 users The BER performance of all the interleavers including Prime Interleaver 48 users Random Interleaver 64 users random interleaver and tree based interleaver is almost similar. -6 10 Prime Interleaver 64 users However, entertaining the other issues including memory and 2 4 6 8 Eb/No 10 12 14 16 bandwidth requirements, the proposed interleavers seems to be optimum and can take the place of the random or any other Figure 3. 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